(1) Field of the Invention
The present invention relates to structural optimization systems and more particularly to a structural optimization system which supports design work concerning structural vibrations.
(2) Description of the Related Art
A structure such as a mechanical apparatus has a specific frequency of vibration at which vibration increases when a force is applied, and at this frequency of vibration, the structure vibrates in a specific deformation pattern. This frequency of vibration is called natural frequency and this deformation pattern is called natural vibration mode. There are many combinations of natural frequencies and natural vibration modes in structures. When a natural frequency is very close to the frequency of a force being applied, resonance may occur where vibration is very large. Therefore, a computer-aided design which prevents resonance is generally pursued in designing a structure such as a mechanical apparatus.
In design concerning structural vibrations, a natural vibration mode which is likely to cause resonance must be tracked and the natural frequency corresponding to the natural vibration mode being tracked is set as a target value. In this process, calculation methods including the finite element method are used so that the final structure is determined through repeated computer-aided design (geometrical) model changes using, as parameters, many design variables such as structural size and positions and quantities of components. This is a common problem which often arises in designing a structure such as a mechanical apparatus.
Since a parameter survey for design of an actual structure usually requires considerable cost in terms of both time and labor, automation of this process as described in Japanese Patent Application Laid-Open Publication No. H10-207926 is effective. In the structural optimization system disclosed in Japanese Patent Application Laid-Open Publication No. H10-207926 (design support system for structures and the like), a parameter survey for issues related to statics is automated.
A popular method of tracking a specific natural vibration mode is that as described in Japanese Patent Application Laid-Open Publication No. 2004-70397, a natural vibration mode is regarded as a vector and a natural vibration mode which has the highest correlativity according to the value of inner product is tracked.
Natural vibration modes as calculation results obtained by a calculation method like the finite element method are outputted in the descending order of natural frequency. As for the problem of vibration, when a design variable is changed, the order of occurrence among many natural vibration modes may change. Taking a cantilever beam as an example, how the order of occurrence of natural vibration modes changes will be explained below with reference to FIG. 15. As the plate width of the cantilever beam becomes smaller, the natural frequency of the natural vibration mode for bending decreases and the natural frequency of the natural vibration mode for torsion increases. Contrariwise, as the plate width of the cantilever beam becomes larger, the natural frequency of the natural vibration mode for bending increases and the natural frequency of the natural vibration mode for torsion decreases. Thus, the order of occurrence of natural vibration modes changes depending on the cantilever beam plate width. Therefore, in order to find a structure in which the natural frequency of the natural vibration mode which easily causes resonance is far different from the exciting frequency, a specific vibration mode should be pursued and tracked through repeated computer-aided design model changes. However, the structural optimization system described in Japanese Patent Application Laid-Open Publication No. H10-207926, which does not involve this kind of natural vibration mode tracking, is not satisfactory in addressing the vibration problem.
One method of tracking a specific natural vibration mode is to investigate a natural vibration mode with the highest correlativity according to the value of inner product square where a natural vibration mode is regarded as a vector as described in Japanese Patent Application Laid-Open Publication No. 2004-70397. However, this method is not suitable for use in calculation methods widely used in structural optimization design such as the finite element method. More specifically, in a calculation method in which a discrete physical model is substituted for a structure as an object, like the finite element method, equations are represented on a discrete space lattice (space lattice is called mesh and points constituting the lattice are called nodes). In this method, when a computer-aided design model is changed, nodes are renumbered as shown in FIG. 16. For this reason, it is hard to say that it is always useful to use an algorithm for tracking natural vibration modes by squaring the inner product.